Question

QNO 3:-In the given figure line AB and CD intersect at O. <BOC =36º.Find <x, y and <z.

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Answer 1

• Measure of x is 36°
• Measure of y is 144°.
• Measure of z is 144°.

Step-by-step explanation:

To find:-

• Measure of x, y and z.

Solution:-

We know that,

Angles forms when two lines intersect or bisect each other than their vertical opposite angles are equal. This property is known as 'Vertically opposite angles' .

So,

x = 36°.

We also know that,

Sum of all angles forms on straight line is equal to 180°. This statement is known as linear pair.

So,

➞ x + y = 180°

➞ 36° + y = 180°

➞ y = 180° - 36°

➞ y = 144°

Similarly,

➞x + z = 180°

➞ 36° + z = 180°

➞ z = 180° - 36°

➞ z = 144°

Therefore,

Measure of x is 36°

Measure of y is 144°.

Measure of z is 144°.

Answer 2

$\huge\bold{{\fcolorbox{lime}{lime}{Answer~~~↓}}}$

$\small{ }$

$\large\bold{{\underline{\underline{\green{To~find:}}}}}$

The value of the unknown angles : x, y and z

$\large\bold{{\underline{\underline{\green{Here:}}}}}$

$\large\mathtt{x={\underline{\underline{36°}}}}$ (Vertically opposite angles)

$\large\implies\mathtt{z+36°=180°}$ (Linear pair)

$\large\implies\mathtt{z=180-36}$

$\large\implies\mathtt{z={\underline{\underline{144°}}}}$

$\large\bold{{\underline{\underline{\green{Also:}}}}}$

$\large\implies\mathtt{y+36°=180°}$ (Linear pair)

$\large\implies\mathtt{y=180-36}$

$\large\implies\mathtt{y={\underline{\underline{144°}}}}$

$\small{ }$

$\large\therefore\bold{{\underline{\underline{\green{Required~answer:}}}}}$

• x = 36°
• y = 144°
• z = 144°

$\small{ }$

$\huge\bold\green{★Hope~it~helps..!!}$